Fogel, T.B., Lucky, S.S., Mandy, J.A. and Wellbirth, B.B. 2019. Reducing the PDEs to ODEs through lie vectors using the integrated factors. International research journal of management, IT and social sciences. 6, 5 (Sep. 2019), 193–203. DOI:https://doi.org/10.21744/irjmis.v6n5.732.